CERN-PH-EP/2015-285 2016/04/14
CMS-HIG-14-028
Measurement of differential and integrated fiducial cross
sections for Higgs boson production in the four-lepton
decay channel in pp collisions at
√
s
=
7 and 8 TeV
The CMS Collaboration
∗Abstract
Integrated fiducial cross sections for the production of four leptons via the H → 4`
decays (` = e, µ) are measured in pp collisions at√s = 7 and 8 TeV. Measurements
are performed with data corresponding to integrated luminosities of 5.1 fb−1at 7 TeV,
and 19.7 fb−1 at 8 TeV, collected with the CMS experiment at the LHC. Differential
cross sections are measured using the 8 TeV data, and are determined as functions of the transverse momentum and rapidity of the four-lepton system, accompanying jet multiplicity, transverse momentum of the leading jet, and difference in rapidity
between the Higgs boson candidate and the leading jet. A measurement of the Z→4`
cross section, and its ratio to the H → 4` cross section is also performed. All cross
sections are measured within a fiducial phase space defined by the requirements on
lepton kinematics and event topology. The integrated H→4`fiducial cross section is
measured to be 0.56+−0.670.44(stat) +−0.210.06(syst) fb at 7 TeV, and 1.11+−0.410.35(stat) +−0.140.10(syst) fb at 8 TeV. The measurements are found to be compatible with theoretical calculations based on the standard model.
Published in the Journal of High Energy Physics as doi:10.1007/JHEP04(2016)005.
c
2016 CERN for the benefit of the CMS Collaboration. CC-BY-3.0 license
∗See Appendix A for the list of collaboration members
1
Introduction
The observation of a new boson consistent with the standard model (SM) Higgs boson [1–6] was reported by the ATLAS and CMS collaborations in 2012 [7, 8]. Subsequent measurements confirmed that the properties of the new boson, such as its couplings and decay width, are in-deed consistent with expectations for the SM Higgs boson [9–13] (and references given therein). In this paper we present measurements of the integrated and differential cross sections for the
production of four leptons via the H→ 4`decays (` = e, µ) in pp collisions at centre-of-mass
energies of 7 and 8 TeV. All cross sections are measured in a restricted part of the phase space (fiducial phase space) defined to match the experimental acceptance in terms of the lepton
kinematics and topological event selection. The H → 4` denotes the Higgs boson decay to
the four-lepton final state via an intermediate pair of neutral electroweak bosons. A similar
study of the Higgs boson production cross section using the H→4`decay channel has already
been performed by the ATLAS Collaboration [14], while measurements in the H → 2γ decay
channel have been reported by both the ATLAS and CMS collaborations [15, 16].
The integrated fiducial cross sections are measured using pp collision data recorded with the
CMS detector at the CERN LHC corresponding to integrated luminosities of 5.1 fb−1 at 7 TeV
and 19.7 fb−1 at 8 TeV. The measurement of the ratio of cross sections at 7 and 8 TeV is also
performed. The differential fiducial cross sections are measured using just the 8 TeV data, due to the limited statistics of the 7 TeV data set. The cross sections are corrected for effects related to detector efficiency and resolution. The fiducial phase space constitutes approximately 42% of the total available phase space, and there is no attempt to extrapolate the measurements to the full phase space. This approach is chosen to reduce the systematic uncertainty associated with the underlying model of the Higgs boson properties and production mechanism. The remaining dependence of each measurement on the model assumptions is determined and quoted as a separate systematic effect. Due to the strong dependence of the cross section times
branching fraction on the mass of the Higgs boson (mH) in the region around 125 GeV, the
measurements are performed assuming a mass of mH = 125.0 GeV, as measured by the CMS
experiment using the H →4`and H →2γ channels [11]. This approach also allows an easier
comparison of measurements with the theoretical estimations.
The differential fiducial cross sections are measured as a function of several kinematic observ-ables that are sensitive to the Higgs boson production mechanism: transverse momentum and rapidity of the four-lepton system, transverse momentum of the leading jet, separation in ra-pidity between the Higgs boson candidate and the leading jet, as well as the accompanying jet
multiplicity. In addition, measurements of the Z → 4`fiducial cross section, and of its ratio
to the corresponding H → 4`fiducial cross section are also performed using the 8 TeV data.
These measurements provide tests of the SM expectations, and important validations of our
understanding of the detector response and methodology used for the H → 4`cross section
measurement. The results of the H→4`cross section measurements are compared to
theoret-ical calculations in the SM Higgs sector that offer up to next-to-next-to-leading-order (NNLO) accuracy in perturbative QCD, and up to next-to-leading-order (NLO) accuracy in perturbative electro-weak corrections.
All measurements presented in this paper are based on the experimental techniques used in previous measurements of Higgs boson properties in this final state [17, 18]. These techniques include: algorithms for the online event selection, algorithms for the reconstruction, identi-fication and calibration of electrons, muons and jets, as well as the approaches to the event selection and background estimation.
2 3 Data and simulation samples
This paper is organized as follows. The CMS detector and experimental techniques are briefly described in Section 2. The data sets and simulated samples used in the analysis are described in Section 3. The event selection and background modelling are presented in Section 4. The fiducial phase space used for the measurements is defined in Section 5, while the procedure for extracting the integrated and differential cross sections is presented in Section 6. Section 7 discusses the systematic uncertainties in the measurements. Section 8 presents the results of all measurements and their comparison with the SM-based calculations.
2
The CMS detector and experimental methods
The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diame-ter, providing a magnetic field of 3.8 T. Within the solenoid volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter, and a brass and scintillator hadron calorimeter, each composed of a barrel and two endcap sections. Forward calorimetry extends
the pseudorapidity coverage provided by the barrel and endcap detectors to|η| < 5. Muons
are measured in gas-ionization detectors embedded in the steel flux-return yoke outside the solenoid. A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [19].
The reconstruction of particles emerging from each collision event is obtained via a particle-flow event reconstruction technique. The technique uses an optimized combination of all in-formation from the CMS sub-detectors to identify and reconstruct individual particles in the collision event [20, 21]. The particles are classified into mutually exclusive categories: charged hadrons, neutral hadrons, photons, muons, and electrons. Jets are reconstructed from the
in-dividual particles using the anti-kT clustering algorithm with a distance parameter of 0.5 [22],
as implemented in theFASTJETpackage [23, 24]. Energy deposits from the multiple pp
interac-tions (pileup) and from the underlying event are subtracted when computing the energy of jets
and isolation of reconstructed objects using the FASTJETtechnique [24–26].
Details on the experimental techniques for the reconstruction, identification, and isolation of electrons, muons and jets, as well as on the efficiencies of these techniques can be found in Refs. [21, 27–32]. Details on the procedure used to calibrate the leptons and jets in this analysis can be found in Ref. [17].
3
Data and simulation samples
The data set analyzed was collected by the CMS experiment in 2011 and 2012, and corresponds
to integrated luminosities of 5.1 fb−1of 7 TeV collision data and 19.7 fb−1of 8 TeV collision data,
respectively. The set of triggers used to collect the data set is the same as the one used in previous measurements of Higgs boson properties in four-lepton final states [17, 18].
Descriptions of the SM Higgs boson production in the gluon fusion (gg → H) process are
obtained using the HRES 2.3 [33, 34], POWHEG V2 [35, 36], and POWHEG MINLO HJ [37]
generators. The HRESgenerator is a partonic level Monte Carlo (MC) generator that provides
a description of the gg → H process at NNLO accuracy in perturbative QCD and
next-to-next-to-leading-logarithmic (NNLL) accuracy in the resummation of soft-gluon effects at small transverse momenta [33, 34]. Since the resummation is inclusive over the QCD radiation
recoil-ing against the Higgs boson, HRESis considered for the estimation of fiducial cross sections
that are inclusive in the associated jet activity. The HRESestimations are obtained by choosing
POWHEGgenerator is a partonic level matrix-element generator that implements NLO pertur-bative QCD calculations and additionally provides an interface with parton shower programs.
It provides a description of the gg → H production in association with zero jets at NLO
ac-curacy. For the purpose of this analysis, it has been tuned using thePOWHEGdamping factor
hdump of 104.16 GeV, to closely match the Higgs boson pTspectrum in the full phase space, as
estimated by the HRESgenerator. This factor minimises emission of the additional jets in the
limit of large pT, and enhances the contribution from the Sudakov form factor as pTapproaches
zero [35, 36]. The POWHEGMINLO HJ generator is an extension of the POWHEG V2 generator
based on the MINLO prescription [37] for the improved next-to-leading-logarithmic accuracy
applied to the gg → H production in association with up to one additional jet. It provides a
description of the gg → H production in association with zero jets and one jet at NLO
accu-racy, and the gg → H production in association with two jets only at the leading-order (LO)
accuracy. All the generators used to describe the gg → H process take into account the finite
masses of the bottom and top quarks. The description of the SM Higgs boson production in the
vector boson fusion (VBF) process is obtained at NLO accuracy using thePOWHEG generator.
The processes of SM Higgs boson production associated with gauge bosons (VH) or top
quark-antiquark pair (ttH) are described at LO accuracy using PYTHIA 6.4 [38]. The MC samples
simulated with these generators are normalized to the inclusive SM Higgs boson production cross sections and branching fractions that correspond to the SM calculations at NNLO and NNLL accuracy, in accordance with the LHC Higgs Cross Section Working Group
recommen-dations [39].ThePOWHEGsamples of the gg→H and VBF processes are used together with the
PYTHIAsamples of the VH and ttH processes to model the SM signal acceptance in the fiducial phase space and to extract the results of the fiducial cross section measurements following the
method described in Section 6. These samples, together with the HRESand POWHEGMINLO
HJ samples of the alternative description of the gg → H process, are used to compare the
measurement results to the SM-based theoretical calculations in Section 8.
In order to estimate the dependence of the measurement procedure on the underlying assump-tion for the Higgs boson producassump-tion mechanism, we have used the set of MC samples for individual production mechanisms described in the previous paragraph. In addition, in order to estimate the dependence of the measurement on different assumptions of the Higgs boson properties, we have also simulated a range of samples that describe the production and decay of exotic Higgs-like resonances to the four-lepton final state. These include zero, spin-one, and spin-two resonances with anomalous interactions with a pair of neutral gauge bosons
(ZZ, Zγ∗, γ∗γ∗) described by higher-order operators, as discussed in detail in Ref. [18]. All of
these samples are generated using thePOWHEGgenerator for the description of NLO QCD
ef-fects in the production mechanism, and JHUGEN[40–42] to describe the decay of these exotic
resonances to four leptons including all spin correlations.
The MC event samples that are used to estimate the contribution from the background process
gg →ZZ are simulated using MCFM 6.7 [43], while the background process qq →4`is
sim-ulated at NLO accuracy with thePOWHEGgenerator including s-, t-, and u-channel diagrams.
For the purpose of the Z→ 4`cross section measurements, we have also separately modelled
contributions from the t- and u-channels of the qq(→ ZZ∗) → 4` process at NLO accuracy
withPOWHEG.
All the event generators described above take into account the initial- and final-state QED ra-diation (FSR) effects which can lead to the presence of additional hard photons in an event.
Furthermore, the POWHEG and JHUGENevent generators take into account interference
be-tween all contributing diagrams in the H → 4` process, including those related to the
4 4 Event selection and background modelling
NNLO generators, the sets of parton distribution functions (PDF) CTEQ6L [44], CT10 [45], and MSTW2008 [46] are used, respectively.
All generated events are interfaced with PYTHIA 6.4.26 Tune Z2∗ to simulate the effects of
the parton shower, multi-parton interactions, and hadronization. The PYTHIA 6.4.26 Z2∗ tune
is derived from the Z1 tune [47], which uses the CTEQ5L parton distribution set, whereas
Z2∗ adopts CTEQ6L [48]. The HRESgenerator does not provide an interface with programs
that can simulate the effects of hadronization and multi-parton interactions. In order to
ac-count for these effects in the HRESestimations, the HRES generator is used to first reweight
the POWHEG+JHUGENevents simulated without multi-parton interaction and hadronization
effects in a phase space that is slightly larger than the fiducial phase space. After that, the
multi-parton interaction and hadronization effects are simulated using PYTHIA and the reweighted
POWHEG+JHUGENevents. The reweighting is performed separately for each observable of interest for the differential, as well as for the integrated cross section measurements. This
pro-cedure effectively adds the non-perturbative effects to the HRESpartonic level estimations.
The generated events are processed through a detailed simulation of the CMS detector based
on GEANT4 [49, 50] and are reconstructed with the same algorithms that are used for data
analysis. The pileup interactions are included in simulations to match the distribution of the number of interactions per LHC bunch crossing observed in data. The average number of pileup interactions is measured to be approximately 9 and 21 in the 7 and 8 TeV data sets, respectively.
The selection efficiency in all the simulated samples is rescaled to correct for residual differ-ences in lepton selection efficiencies in data and simulation. This correction is based on the total lepton selection efficiencies measured in inclusive samples of Z boson events in simula-tion and data using a “tag-and-probe” method [29], separately for 7 and 8 TeV collisions. More details can be found in Ref. [17].
4
Event selection and background modelling
The measurements presented in this paper are based on the event selection used in the pre-vious measurements of Higgs boson properties in this final state [17, 18]. Events are selected online requiring the presence of a pair of electrons or muons, or a triplet of electrons. Triggers
requiring an electron and a muon are also used. The minimum pTof the leading and
sublead-ing lepton are 17 and 8 GeV, respectively, for the double-lepton triggers, while they are 15, 8 and 5 GeV for the triple-electron trigger. Events with at least four well identified and isolated electrons or muons are then selected offline, if they are compatible with being produced at the
primary vertex. The primary vertex is selected to be the one with the highest sum of p2Tof
asso-ciated tracks. Among all same-flavour and opposite-sign (SFOS) lepton pairs in the event, the
one with an invariant mass closest to the nominal Z boson mass is denoted Z1 and retained if
its mass, m(Z1), satisfies 40≤m(Z1) ≤120 GeV. The remaining leptons are considered and the
presence of a second`+`−pair, denoted Z2, is required with condition 12≤ m(Z2) ≤120 GeV.
If more than one Z2candidate satisfies all criteria, the pair of leptons with the largest sum of the
transverse momenta magnitudes,Σ|pT|, is chosen. Among the four selected leptons`i(i=1..4)
forming the Z1 and Z2candidates, at least one lepton should have pT ≥ 20 GeV, another one
pT ≥ 10 GeV, and any opposite-charge pair of leptons`+i and`
−
j , irrespective of flavor, must
satisfy m(`+i `−j ) ≥ 4 GeV. The algorithm to recover the photons from the FSR uses the same
procedure as described in Ref. [17].
mea-surements as a function of jet-related observables. Jets are selected if they satisfy pT ≥30 GeV
and|η| ≤4.7, and are required to be separated from the lepton candidates and from identified
FSR photons by∆R≡√(∆η)2+ (∆φ)2>0.5 (where φ is the azimuthal angle in radians) [17].
After the event selection is applied, the dominant contribution to the irreducible background
for the H → 4` process originates from the ZZ production via the qq annihilation, while the
subdominant contribution arises from the ZZ production via gluon fusion. In those processes, at least one of the intermediate Z bosons is not on-shell. The reducible backgrounds mainly arise from the processes where parts of intrinsic jet activity are misidentified as an electron or a muon, such as: production of Z boson in association with jets, production of a ZW boson pair in association with jets, and the tt pair production. Hereafter, this background is denoted as
Z+X. The other background processes have negligible contribution.
In the case of the H → 4` cross section measurements, the irreducible qq → ZZ and gg →
ZZ backgrounds are evaluated from simulation based on generators discussed in Section 3,
following Ref. [17]. In the case of the gg→ZZ background, the LO cross section of gg→ZZ is
corrected via a m4`dependent k-factor, as recommended in the study of Ref. [51].
Table 1: The number of estimated background and signal events, as well as the number of
observed candidates, after final inclusive selection in the range 105< m4` < 140 GeV, used in
the H→ 4`measurements. Signal and ZZ background are estimated from simulations, while
the Z+X background is evaluated using control regions in data.
Channel 4e 4µ 2e2µ
5.1 fb−1(7 TeV)
qq→ZZ 0.8±0.1 1.8±0.1 2.2±0.3
Z+X 0.3±0.1 0.2±0.1 1.0±0.3
gg→ZZ 0.03±0.01 0.06±0.02 0.07±0.02
Total background expected 1.2±0.1 2.1±0.1 3.4±0.4
H→4`(mH =125.0 GeV) 0.7±0.1 1.2±0.1 1.7±0.3 Observed 1 3 6 19.7 fb−1(8 TeV) qq→ZZ 3.0±0.4 7.6±0.5 9.0±0.7 Z+X 1.5±0.3 1.2±0.5 4.2±1.1 gg→ZZ 0.2±0.1 0.4±0.1 0.5±0.1
Total background expected 4.8±0.7 9.2±0.7 13.7±1.3
H→4`(mH =125.0 GeV) 2.9±0.4 5.6±0.7 7.3±0.9
Observed 9 15 15
The reducible background (Z+X) is evaluated using the method based on lepton
misidentifi-cation probabilities and control regions in data, following the procedure described in Ref. [17].
In the case of the integrated H → 4` cross section measurement, the shape of the m4`
distri-bution for the reducible background is obtained by fitting the m4` with empirical analytical
functional forms presented in Ref. [17]. In the case of the differential H → 4`measurements,
the shapes of the reducible background are obtained from the control regions in data in the form of template functions, separately for each bin of the considered observable. The template functions are prepared following a procedure described in the spin-parity studies presented in Refs. [17, 18].
The number of estimated signal and background events for the H →4`measurement, as well
6 5 Fiducial phase space definition
region 105<m4` <140 GeV are given in Table 1, separately for 7 and 8 TeV.
In part of the m4`spectrum below 100 GeV, the dominant contribution arises from the resonant
Z → 4` production (s-channel of the qq → 4` process via the Z boson exchange). The
sub-dominant contributions arise from the corresponding t- and u-channels of the qq→4`process,
from the reducible background processes (Z+X), as well as from the gg→ZZ background. In
the case of the Z→4`measurements, contributions from s-, t-, and u-diagrams of the qq→4`
process (and their interference), and contribution of the gg → ZZ process are estimated from
simulation. The Z+X background is evaluated using control regions in data following an
identical procedure as the one described above. The expected number of events arising from
the s-channel of the qq→4`process is 57.4±0.3, from all other SM processes is 3.6±0.5, and
72 candidate events are observed after the final inclusive selection in 8 TeV data in the mass
region 50<m4` <105 GeV.
The reconstructed four-lepton invariant mass distributions in the region of interest for the H→
4` and Z → 4`measurements (50 < m4` < 140 GeV) are shown in Fig. 1 for the 7 and 8 TeV
data sets, and compared to the SM expectations.
[GeV] 4l m 50 60 70 80 90 100 110 120 130 140 Events / (3 GeV) 0 1 2 3 4 5 6 7 8 9 10 11 Data * γ ZZ/Z Z+X =125 GeV H m (7 TeV) -1 5.1 fb CMS [GeV] 4l m 50 60 70 80 90 100 110 120 130 140 Events / (3 GeV) 0 5 10 15 20 25 30 35 Data * γ ZZ/Z Z+X =125 GeV H m (8 TeV) -1 19.7 fb CMS
Figure 1: Distributions of the m4` observable in 7 TeV (left) and 8 TeV (right) data, as well as
expectations for the SM Higgs boson (mH = 125.0 GeV) and other contributing SM processes,
including resonant Z→4`decays.
5
Fiducial phase space definition
The acceptance and selection efficiency for the H → 4`decays can vary significantly between
different Higgs boson production mechanisms and different exotic models of Higgs boson properties. In processes with large jet activity (such as the ttH production), or with low
in-variant mass of the second lepton pair (such as H → Zγ∗(γ∗γ∗) → 4` processes), or with
the H → 4` kinematics different from the SM estimation (such as exotic Higgs-like spin-one
models), the inclusive acceptance of signal events can differ by up to 70% from the inclusive
acceptance estimated for SM H→4`decays.
In order to minimise the dependence of the measurement on the specific model assumed for
Higgs boson production and properties, the fiducial phase space for the H → 4`cross section
measurements is defined to match as closely as possible the experimental acceptance defined by the reconstruction-level selection. This includes the definition of selection observables and selection requirements, as well as the definition of the algorithm for the topological event se-lection.
The fiducial phase space is defined using the leptons produced in the hard scattering, before any FSR occurs. This choice is motivated by the fact that the recovery of the FSR photons is explicitly performed at the reconstruction level. In the case of differential measurements as a function of jet-related observables, jets are reconstructed from the individual stable particles,
excluding neutrinos and muons, using the anti-kt clustering algorithm with a distance
param-eter of 0.5. Jets are considered if they satisfy pT ≥30 GeV and|η| ≤4.7.
The fiducial phase space requires at least four leptons (electrons, muons), with at least one
lepton having pT > 20 GeV, another lepton having pT > 10 GeV, and the remaining electrons
and muons having pT > 7 GeV and pT > 5 GeV respectively. All electrons and muons must
have pseudorapidity|η| <2.5 and|η| <2.4, respectively. In addition, each lepton must satisfy
an isolation requirement computed using the pT sum of all stable particles within ∆R < 0.4
distance from that lepton. The pT sum excludes any neutrinos, as well as any photon or stable
lepton that is a daughter of the lepton for which the isolation sum is being computed. The
ratio of this sum and the pT of the considered lepton must be less than 0.4, in line with the
requirement on the lepton isolation at the reconstruction level [17]. The inclusion of isolation is an important step in the fiducial phase space definition as it reduces significantly the dif-ferences in signal selection efficiency between different signal models. It has been verified in simulation that the signal selection efficiency differs by up to 45% between different models if the lepton isolation requirement is not included. This is especially pronounced in case of large associated jet activity as in the case of ttH production mode. Exclusion of neutrinos and FSR photons from the computation of the isolation sum brings the definition of the fiducial phase space closer to the reconstruction level, and improves the model independence of the signal selection efficiency by an additional few percent.
Furthermore, an algorithm for a topological selection closely matching the one at the recon-struction level is applied as part of the fiducial phase space definition. At least two SFOS lepton pairs are required, and all SFOS lepton pairs are used to form Z boson candidates. The SFOS pair with invariant mass closest to the nominal Z boson mass (91.188 GeV) is taken
as the first Z boson candidate (denoted as Z1). The mass of the Z1 candidate must satisfy
40 < m(Z1) < 120 GeV. The remaining set of SFOS pairs are used to form the second Z boson
candidate (denoted as Z2). In events with more than one Z2candidate, the SFOS pair with the
largest sum of the transverse momenta magnitudes,Σ|pT|, is chosen. The mass of the Z2
candi-date must satisfy 12<m(Z2) <120 GeV. Among the four selected leptons, any pair of leptons
`iand`jmust satisfy∆R(`i`j) >0.02. Similarly, of the four selected leptons, the invariant mass
of any opposite-sign lepton pair must satisfy m(`+i `−j ) >4 GeV. Finally, the invariant mass of
the Higgs boson candidate must satisfy 105 < m4` < 140 GeV. The requirement on the m4`
is important as the off-shell production cross section in the dominant gluon fusion production mode is sizeable and can amount up to a few percent of the total cross section [52]. All the requirements and selections used in the definition of the fiducial phase space are summarised in Table 2.
It has been verified in simulation that the reconstruction efficiency for events originating from the fiducial phase space defined in this way only weakly depends on the Higgs boson prop-erties and production mechanism. The systematic effect associated with the remaining model dependence is extracted and quoted separately, considering a wide range of alternative Higgs boson models, as described in Section 7. The fraction of signal events within the fiducial phase
spaceAfid, and the reconstruction efficiency e for signal events within the fiducial phase space
for individual SM production modes and exotic signal models are listed in Table 3.
8 5 Fiducial phase space definition
Table 2: Summary of requirements and selections used in the definition of the fiducial phase
space for the H → 4` cross section measurements. For measurements of the Z → 4` cross
section and the ratio of the H→4`and Z→4`cross sections, the requirement on the invariant
mass of the selected four leptons is modified accordingly. More details, including the exact
definition of the stable particles and lepton isolation, as well as Z1 and Z2 candidates, can be
found in the text.
Requirements for the H→4`fiducial phase space
Lepton kinematics and isolation
Leading lepton pT pT >20 GeV
Sub-leading lepton pT pT >10 GeV
Additional electrons (muons) pT pT >7(5)GeV
Pseudorapidity of electrons (muons) |η| <2.5(2.4)
Sum of scalar pTof all stable particles within∆R<0.4 from lepton <0.4pT
Event topology
Existence of at least two SFOS lepton pairs, where leptons satisfy criteria above
Inv. mass of the Z1candidate 40< m(Z1) <120 GeV
Inv. mass of the Z2candidate 12< m(Z2) <120 GeV
Distance between selected four leptons ∆R(`i`j) >0.02
Inv. mass of any opposite-sign lepton pair m(`+i `−j ) >4 GeV
Inv. mass of the selected four leptons 105<m4` <140 GeV
Table 3: The fraction of signal events within the fiducial phase space (acceptance Afid),
re-construction efficiency (e) for signal events from within the fiducial phase space, and ratio of reconstructed events which are from outside the fiducial phase space to reconstructed events
which are from within the fiducial phase space ( fnonfid). Values are given for characteristic
signal models assuming mH = 125.0 GeV,
√
s = 8 TeV, and the uncertainties include only the
statistical uncertainties due to the finite number of events in MC simulation. In case of the first seven signal models, decays of the Higgs-like boson to four leptons proceed according to
SM via the H → ZZ∗ → 4` process. Definition of signal excludes events where at least one
reconstructed lepton originates from associated vector bosons or jets. The factor(1+ fnonfid)e
is discussed in Section 6.
Signal process Afid e fnonfid (1+ fnonfid)e
Individual Higgs boson production modes
gg→H (POWHEG+JHUGEN) 0.422±0.001 0.647±0.002 0.053±0.001 0.681±0.002
VBF (POWHEG) 0.476±0.003 0.652±0.005 0.040±0.002 0.678±0.005
WH (PYTHIA) 0.342±0.002 0.627±0.003 0.072±0.002 0.672±0.003
ZH (PYTHIA) 0.348±0.003 0.634±0.004 0.072±0.003 0.679±0.005
ttH (PYTHIA) 0.250±0.003 0.601±0.008 0.139±0.008 0.685±0.010 Some characteristic models of a Higgs-like boson with exotic decays and properties qq→H(JCP =1−)(JHUGEN) 0.238±0.001 0.609±0.002 0.054±0.001 0.642±0.002
qq→H(JCP =1+)(JHUGEN) 0.283±0.001 0.619±0.002 0.051±0.001 0.651±0.002 gg→H→Zγ∗(JHUGEN) 0.156±0.001 0.622±0.002 0.073±0.001 0.667±0.002 gg→H→γ∗γ∗(JHUGEN) 0.188±0.001 0.629±0.002 0.066±0.001 0.671±0.002
of four leptons via the H → 4`decays. This definition excludes events where at least one
decays. Those events present a broad m4`distribution, whose exact shape depends on the pro-duction mode, and are treated as a combinatorial signal-induced background in the measure-ment procedure. This approach provides a simple measuremeasure-ment procedure with a substantially reduced signal model dependence. More details are discussed in Section 6.
In the case of the independent measurement of the Z → 4`fiducial cross section, the fiducial
phase space is defined in the analogous way, with the difference that the invariant mass of the
4`candidate for the Z boson must satisfy 50< m4` <105 GeV. In the case of the measurement
of the ratio of the H→4`and Z→4`cross sections, the mass window of 50<m4` <140 GeV
is used.
6
Measurement methodology
The aim is to determine the integrated and differential cross sections within the fiducial phase space, corrected for the effects of limited detection efficiencies, resolution, and known sys-tematic biases. In order to achieve this goal, we estimate those effects using simulation and
include them in the parameterization of the expected m4` spectra at the reconstruction level.
We then perform a maximum likelihood fit of the signal and background parameterizations to
the observed 4`mass distribution, Nobs(m4`), and directly extract the fiducial cross sections of
interest (σfid) from the fit. In this approach all systematic uncertainties are included in the form
of nuisance parameters, which are effectively integrated out in the fit procedure. The results of measurements are obtained using an asymptotic approach [53] with the test statistics based on the profile likelihood ratio [54]. The coverage of the quoted intervals obtained with this approach has been verified for a subset of results using the Feldman-Cousins method [55]. The maximum likelihood fit is performed simultaneously in all final states and in all bins of the
observable considered in the measurement, assuming a Higgs boson mass of mH =125.0 GeV.
The integrated cross section measurement is treated as a special case with a single bin. This implementation of the procedure for the unfolding of the detector effects from the observed distributions is different from the implementations commonly used in the experimental mea-surements, such as those discussed in Ref. [56], where signal extraction and unfolding are per-formed in two separate steps. It is similar to the approach adopted in Ref. [16].
The shape of the resonant signal contribution,Pres(m4`), is described by a double-sided
Crys-tal Ball function as detailed in Ref. [17], with a normalization proportional to the fiducial cross
section σfid. The shape of the combinatorial signal contribution,Pcomb(m4`), from events where
at least one of the four leptons does not originate from the H →4`decay, is empirically
mod-elled by a Landau distribution whose shape parameters are constrained in the fit to be within a range determined from simulation. The remaining freedom in these parameters results in an additional systematic uncertainty on the measured cross sections. This contribution is treated as a background and hereafter we refer to this contribution as the “combinatorial signal”
con-tribution. This component in the mass range 105<m4` <140 GeV amounts to about 4%, 18%,
and 22% for WH, ZH, and ttH production modes, respectively.
An additional resonant signal contribution from events that do not originate from the fiducial phase space can arise due to detector effects that cause differences between the quantities used for the fiducial phase space definition, such as the lepton isolation, and the analogous quantities used for the event selection. This contribution is also treated as background, and hereafter we refer to this contribution as the “nonfiducial signal” contribution. It has been verified in simulation that the shape of these events is identical to the shape of the resonant fiducial signal and, in order to minimise the model dependence of the measurement, its normalization is fixed to be a fraction of the fiducial signal component. The value of this fraction, which we denote by
10 6 Measurement methodology
fnonfid, has been determined from simulation for each of the studied signal models, and it varies
from∼5% for the gg→H production to∼14% for the ttH production mode. The variation of
this fraction between different signal models is included in the model dependence estimation.
The value of fnonfidfor different signal models is shown in Table 3.
In order to compare with the theoretical estimations, the measurement needs to be corrected for limited detector efficiency and resolution effects. The efficiency for an event passing the fiducial phase space selection to pass the reconstruction selection is measured using signal sim-ulation samples and corrected for residual differences between data and simsim-ulation, as briefly described in Section 3 and detailed in Ref. [17]. It is determined from simulations that this
efficiency for the gg → H process is about 65% inclusively, and that it can vary relative to the
gg → H process by up to∼7% in other signal models, as shown in Table 3. The largest
devi-ations from the overall efficiency that correspond to the SM Higgs boson are found to be from
ttH production, the H→Zγ∗ →4`process, and exotic Higgs-like spin-one models.
In the case of the differential cross section measurements, the finite efficiencies and resolution effects are encoded in a detector response matrix that describes how events migrate from a given observable bin at the fiducial level to a given bin at the reconstruction level. This matrix is diagonally dominant for the jet inclusive observables, but has sizeable off-diagonal elements for the observables involving jets. In the case of the jet multiplicity measurement the next-to-diagonal elements range from 3% to 21%, while in the case of other observables these elements are typically of the order of 1–2%.
Following the models for signal and background contributions described above, the number of expected events in each final state f and in each bin i of a considered observable is expressed as
a function of m4`given by:
Nobsf,i (m4`) =Nfidf,i(m4`) +Nnonfidf,i (m4`) +Ncombf,i (m4`) +Nbkdf,i (m4`)
=
∑
j
efi,j
1+fnonfidf,i σfidf,j L Pres(m4`)
+Ncombf,i Pcomb(m4`) +Nbkdf,i Pbkd(m4`).
(1)
The components Nfidf,i(m4`), Nnonfidf,i (m4`), Ncombf,i (m4`), and Nbkdf,i (m4`) represent the resonant
fiducial signal, resonant nonfiducial signal, combinatorial contribution from fiducial signal,
and background contributions in bin i as functions of m4`, respectively. Similarly, thePres(m4`),
Pcomb(m4`)andPbkd(m4`)are the corresponding probability density functions for the resonant
(fiducial and nonfiducial) signal, combinatorial signal, and background contributions. The efi,j
represents the detector response matrix that maps the number of expected events in a given observable bin j at the fiducial level to the number of expected events in the bin i at the
re-construction level. The fi
nonfidfraction describes the ratio of the nonfiducial and fiducial signal
contribution in bin i at the reconstruction level. The parameter σfidf,j is the signal cross section
for the final state f in bin j of the fiducial phase space.
To extract the 4` fiducial cross-sections, σfid4`,j, in all bins j of a considered observable, an
un-binned likelihood fit is performed simultaneously for all bins i at reconstruction level on the mass distributions of the three final states 4e, 4µ, and 2e2µ, using Eq. (1). In each bin j of the
fiducial phase space the fitted parameters are σfid4`,j, the sum of the three final state cross-sections,
and two remaining degrees of freedom for the relative contributions of the three final states.
The inclusive values of the factor(1+ fnonfid)efrom Eq. (1) are shown in Table 3 for different
factor on the exact signal model is a consequence of the particular definition of the fiducial phase space introduced in Section 5, and enables a measurement with a very small dependence on the signal model.
In the case of the simultaneous fit for the H → 4` signal in 7 and 8 TeV data sets, and the
measurement of the ratio of the H→ 4`cross sections at 7 and 8 TeV, the procedure described
above is generalised to include two separate signals. The parameters extracted simultaneously from the measurement are the 8 TeV fiducial cross section, and ratio of 7 TeV and 8 TeV fiducial cross sections.
In the case of the Z → 4` cross section measurements, the definition of the fiducial phase
space and statistical procedure are analogous to the ones used for the H → 4` cross section
measurements with the Z boson mass fixed to the PDG value of mZ=91.188 GeV [57].
Similarly, in the case of the simultaneous fit for the H → 4` and Z → 4` signals, and the
measurement of the ratio of the H → 4`and Z → 4`cross sections, the procedure described
above is generalised to include two separate signals. The parameters extracted simultaneously
from this measurement are the H → 4` fiducial cross section, and ratio of the H → 4` and
Z→ 4`fiducial cross sections. Furthermore, this measurement is performed in two scenarios.
In the first scenario, we fix the Higgs boson mass to mH = 125.0 GeV and the Z boson mass to
its PDG value. Results of measurements obtained in this scenario are reported in Section 8. In the second scenario, we allow the masses of the two resonances to vary, and we fit for the mass
of the Higgs boson mH and the mass difference between the two bosons∆m =mH−mZ. This
scenario allows for an additional reduction of the systematic uncertainties related to the lepton momentum scale determination, and provides an additional validation of the measurement methodology.
7
Systematic uncertainties
Experimental systematic uncertainties in the parameterization of the signal and the irreducible background processes due to the trigger and combined lepton reconstruction, identification, and isolation efficiencies are evaluated from data and found to be in the range 4–10% [17]. The-oretical uncertainties in the irreducible background rates are estimated by varying the QCD renormalization and factorization scales, and the PDF set following the PDF4LHC
recommen-dations [45, 58–60]. These are found to be 4.5% and 25% for the qq→ ZZ and gg→ZZ
back-grounds, respectively [17]. The systematic uncertainties in the reducible background estimate for the 4e, 4µ, and 2e2µ final states are determined to be 20%, 40%, and 25%, respectively [17]. In the case of the differential measurements, uncertainties in the irreducible background rates are computed for each bin, while uncertainties in the reducible background rates are assumed to be identical in all bins of the considered observable. The absolute integrated luminosity of the pp collisions at 7 and 8 TeV has been determined with a relative precision of 2.2% [61] and 2.6% [62], respectively. For all cross section measurements, an uncertainty in the resolution of the signal mass peak of 20% is included in the signal determination [17].
When measuring the differential cross section as a function of the jet multiplicity, the system-atic uncertainty in the jet energy scale is included as fully correlated between the signal and background estimations. This uncertainty ranges from 3% for low jet multiplicity bins to 12% for the highest jet multiplicity bin for the signal, and from 2% to 16% for background. The uncertainties related to the jet identification efficiency and the jet energy resolution are found to be negligible with respect to the jet energy scale systematic uncertainty.
12 7 Systematic uncertainties
Table 4: Overview of main sources of the systematic uncertainties in the H→ 4`cross section
measurements. More details, including the definition of the model dependence are presented in the text.
Summary of relative systematic uncertainties Common experimental uncertainties
Luminosity 2.2% (7 TeV), 2.6% (8 TeV)
Lepton identification/reconstruction efficiencies 4–10%
Background related uncertainties
QCD scale (qq→ZZ, gg→ZZ) 3–24%
PDF set (qq→ZZ, gg→ZZ) 3–7%
Reducible background (Z+X) 20–40%
Jet resolution and energy scale 2–16%
Signal related uncertainties
Lepton energy scale 0.1–0.3%
Lepton energy resolution 20%
Jet energy scale and resolution 3–12%
Combinatorial signal-induced contribution
Effect on the final measurement 4–11%
Model dependence
With exp. constraints on production modes and exotic models 1–5%
No exp. constraints on production modes and exotic models 7–25%
The underlying assumption on the signal model used to extract the fiducial cross sections in-troduces an additional systematic effect on the measurement result. This effect is estimated by extracting the fiducial cross sections from data assuming a range of alternative signal models. The alternative models include models with an arbitrary fraction of the SM Higgs boson pro-duction modes, models of Higgs-like resonances with anomalous interactions with a pair of neutral gauge bosons, or models of Higgs-like resonances with exotic decays to the four-lepton final state. These exotic models are briefly introduced in Section 3 and detailed in Ref. [18]. The largest deviation between the fiducial cross sections measured assuming these alternative signal models and the fiducial cross section measured under the SM Higgs boson assumption is quoted as the systematic effect associated with the model dependence. If we neglect the existing experimental constraints [11, 18] on the exotic signal models, the effect is found to be up to 7% in all reported measurements, except in the case of the jet multiplicity differential measurement where in some bins the effect can be as large as 25%. If we impose experimen-tal constraints [11, 18] on the allowed exotic signal models, the systematic effect associated with the model dependence reduces to 3-5% for the jet multiplicity differential measurement, and it is smaller than 1% for the other measurements. The more conservative case which does not take into account existing experimental constraints is used to report a separate systematic uncertainty due to the model dependence.
The effect on the cross section measurement due to mHbeing fixed in the fit procedure is
esti-mated from simulation to be about 1%. The additional uncertainty due to this effect is negligi-ble with respect to the other systematic uncertainties, and is not included in the measurements.
The overview of the main systematic effects in the case of the H → 4` measurements is
8
Results
The result of the maximum likelihood fit to the signal and background m4` spectra in data
collected at √s = 8 TeV, used to extract the integrated H → 4`fiducial cross section for the
m4` range from 105 to 140 GeV, is shown in Fig. 2 (left). Similarly, the result of the maximum
likelihood fit for the H→4`and Z→4`contributions to the inclusive m4`spectra in the range
from 50 to 140 GeV is shown in Fig. 2 (right).
[GeV] 4l m 105 110 115 120 125 130 135 140 Events / (2.33 GeV) 0 2 4 6 8 10 12 14 16 18 20 22 Data Combinatorial XH Fiducial Signal ZZ Non-fiducial Signal Z+X (8 TeV) -1 19.7 fb CMS [GeV] 4l m 50 60 70 80 90 100 110 120 130 140 Events / (2 GeV) 0 5 10 15 20 25 30 35 40 (8 TeV) -1 19.7 fb CMS Data Fiducial H→ 4l 4l → Non-fiducial H Combinatorial XH 4l → Fiducial Z Non-fiducial Z→ 4l qqZZ(t-chan.) + ggZZ Z+X
Figure 2: Observed inclusive four-lepton mass distribution and the resulting fits of the signal
and background models, presented in Section 6, in case of an independent H → 4` fit (left)
and a simultaneous H → 4`and Z → 4` fit (right). The gg → H → 4` process is modelled
using POWHEG+JHUGEN, while qq → 4` process is modelled using POWHEG (both s- and
t/u-channels). The sub-dominant component of the Higgs boson production is denoted as XH = VBF + VH + ttH.
Individual measurements of integrated H → 4` fiducial cross sections at 7 and 8 TeV,
per-formed in the m4` range from 105 to 140 GeV, are presented in Table 5 and Fig. 3. The central
values of the measurements are obtained assuming the SM Higgs boson signal with mH =
125.0 GeV, modelled by the POWHEG+JHUGENfor the gg→H contribution,POWHEGfor the
VBF contribution, and PYTHIA for the VH + ttH contributions. In Table 5 and hereafter, the
sub-dominant component of the signal is denoted as XH = VBF + VH + ttH.
The measured fiducial cross sections are compared to the SM NNLL+NNLO theoretical
es-timations in which the acceptance of the dominant gg → H contribution is modelled using
POWHEG+JHUGEN, MINLO HJ, or HRES, as discussed in Section 3. The total uncertainty in the NNLL+NNLO theoretical estimates is computed according to Ref. [39], and includes
un-certainties due to the QCD renormalization and factorization scales (∼7.8%), PDFs and strong
coupling constant αS modelling (∼7.5%), as well as the acceptance (2%) and branching
frac-tion (2%) uncertainties. In the computafrac-tion of the total uncertainty the PDFs/αS uncertainties
are assumed to be correlated between the VBF and VH production modes (dominantly
quark-antiquark initiated), and anticorrelated between the gg→H and ttH production modes
(dom-inantly gluon-gluon initiated). Furthermore, the QCD scale uncertainties are considered to be uncorrelated, while uncertainties in the acceptance and branching fraction are considered to
be correlated across all production modes. The differences in how the POWHEG+JHUGEN,
MINLO HJ, and HRESgenerators model the acceptance of the gg→H contribution are found
to be an order of magnitude lower than the theoretical uncertainties, and in Table 5 and Fig. 3
we show estimations obtained using HRES.
14 8 Results
Table 5: Results of the H→4`integrated fiducial cross section measurements performed in the
m4`range from 105 to 140 GeV for pp collisions at 7 and 8 TeV, and comparison to the theoretical
estimates obtained at NNLL+NNLO accuracy. Statistical and systematic uncertainties, as well as the model-dependent effects are quoted separately. The sub-dominant component of the Higgs boson production is denoted as XH = VBF + VH + ttH.
Fiducial cross section H→4`at 7 TeV
Measured 0.56+−0.670.44(stat)+−0.210.06(syst) ±0.02 (model) fb
gg→H(HRES) + XH 0.93+−0.100.11fb
Fiducial cross section H→4`at 8 TeV
Measured 1.11+−0.410.35(stat)−+0.140.10(syst)+−0.080.02(model) fb
gg→H(HRES) + XH 1.15+−0.120.13fb
Ratio of H→4`fiducial cross sections at 7 and 8 TeV
Measured 0.51+−0.710.40(stat)−+0.130.05(syst)+−0.000.03(model)
gg→H(HRES) + XH 0.805+−0.0030.010
[TeV]
s
7 8 9 10 11 12 13 14[fb]
fidσ
0 0.5 1 1.5 2 2.5 33.5 Data (stat. ⊕ sys. unc.)
Systematic uncertainty Model dependence = 125 GeV) H Standard model (m (8 TeV) -1 (7 TeV), 19.7 fb -1 5.1 fb
CMS
4l) + X → (H → ppFigure 3: Results of measurements of the integrated H → 4`fiducial cross section in pp
col-lisions at 7 and 8 TeV, with a comparison to SM estimates. The red error bar represents the systematic uncertainty, while the black error bar represents the combined statistical and sys-tematic uncertainties, summed in quadrature. The additional syssys-tematic effect associated with model dependence is represented by grey boxes. The theoretical estimates at NNLL+NNLO accuracy and the corresponding systematic uncertainties are shown in blue as a function of
the centre-of-mass energy. The acceptance of the dominant gg → H contribution is modelled
at the parton level using HRES, and corrected for hadronization and underlying-event effects
estimated using POWHEG+JHUGENand PYTHIA6.4.
the theoretical estimations within the associated uncertainties. The uncertainty of the mea-surement is largely dominated by its statistical component of about 37%, while the systematic component is about 12%. The theoretical uncertainty of about 11% is comparable to the sys-tematic uncertainty, and is larger than the model dependence of the extracted results, which
is about 7%. In the case of the cross section at 7 TeV, as well as the ratio of cross sections at 7 and 8 TeV, the measured cross sections are lower but still in agreement with the SM theoretical estimations within the large statistical uncertainties.
Table 6: The Z → 4` integrated fiducial cross section at 8 TeV in the m4` range from 50 to
105 GeV, and the ratio of 8 TeV fiducial cross sections of H → 4`and Z → 4`obtained from a
simultaneous fit of mass peaks of Z→4`and H→4`in the mass window 50 to 140 GeV. The
sub-dominant component of the Higgs boson production is denoted as XH = VBF + VH + ttH.
Fiducial cross section Z→4`at 8 TeV
(50<m4` <105 GeV)
Measured 4.81+−0.690.63(stat)+−0.180.19(syst) fb
POWHEG 4.56±0.19 fb
Ratio of fiducial cross sections of H→4`and Z→4`at 8 TeV
(50<m4` <140 GeV)
Measured 0.21+−0.090.07(stat)±0.01 (syst)
gg→H(HRES) + XH and Z→4`(POWHEG) 0.25±0.04
The result of the measurement of the integrated Z → 4`fiducial cross section at 8 TeV in the
m4` range from 50 to 105 GeV is summarized in Table 6. The measured Z → 4`cross section
is found to be in good agreement with the theoretical estimations obtained usingPOWHEG. As
the total relative uncertainty in the Z → 4` measurement is about 2.6 times lower than the
relative uncertainty in the H → 4`measurement, the good agreement between the measured
and estimated Z → 4` cross section provides a validation of the measurement procedure in
data.
In addition, a simultaneous fit for the H →4`and Z→ 4`resonances is performed in the m4`
range from 50 to 140 GeV, and the ratio of the corresponding fiducial cross sections is extracted. The measurement of the ratio of these cross sections, when masses of the two resonances are fixed in the fit, is presented in Table 6. A good agreement between the measured ratio and its SM theoretical estimation is observed. In the scenario in which the masses of the two res-onances are allowed to vary, as discussed in Section 6, the fitted value for the mass difference
between the two resonances is found to be∆m = mH−mZ = 34.2±0.7 GeV. As discussed in
Ref. [63], it is worth noting that by using the measured mass difference∆m and the PDG value
of the Z boson mass mPDGZ which is precisely determined in other experiments, the Higgs boson
mass can be extracted as mH =mPDGZ +∆m=125.4±0.7 GeV. This result is in agreement with
the best fit value for mHobtained from the dedicated mass measurement in this final state [17],
and provides further validation of the measurement procedure.
The measured differential H → 4`cross sections at 8 TeV, along with the theoretical
estima-tions for a SM Higgs boson with mH = 125.0 GeV are presented in Figs. 4 and 5. Results of
the measurements are shown for the transverse momentum and the rapidity of the four-lepton system, jet multiplicity, transverse momentum of the leading jet, as well as separation in ra-pidity between the Higgs boson candidate and the leading jet. The uncertainty in the
theoret-ical estimation for the dominant gg → H process is computed in each bin of the considered
observable by the generator used for the particular signal description (POWHEG+JHUGEN,
POWHEG MINLO HJ, or HRES). The theoretical uncertainties for the associated production
mechanisms are taken as constant across the bins of the differential observables and are ob-tained from Ref. [39].
pertur-16 8 Results (H) [fb/GeV] T /dp fid σ d -3 10 -2 10 -1 10 1 (8 TeV) -1 19.7 fb CMS sys. unc.) ⊕
Data (stat. gg→H (POWHEG+JHUGen) + XH Systematic uncertainty gg→H (MiNLO HJ) + XH Model dependence gg→H (HRes) + XH
XH = VBF + VH + ttH (H) [GeV] T p 0 20 40 60 80 100 120 140 160 180 200 Ratio to HRes 0 0.5 1 1.5 2 2.5 /d|y(H)| [fb] fid σ d 0.5 1 1.5 2 2.5 3 3.5 (8 TeV) -1 19.7 fb CMS sys. unc.) ⊕
Data (stat. gg→H (POWHEG+JHUGen) + XH Systematic uncertainty gg→H (MiNLO HJ) + XH Model dependence gg→H (HRes) + XH
XH = VBF + VH + ttH |y(H)| 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 Ratio to HRes 0.50 1 1.52 2.53 3.54 4.5
Figure 4: Results of the differential H → 4`fiducial cross section measurements and
compar-ison to the theoretical estimates for the transverse momentum (left) and the rapidity (right) of the four-lepton system. The red error bars represent the systematic uncertainties, while black error bars represent the combined statistical and systematic uncertainties, summed in quadrature. The additional systematic uncertainty associated with the model dependence is separately represented by the grey boxes. Theoretical estimates, in which the acceptance of
the dominant gg → H contribution is modelled by POWHEG+JHUGEN+PYTHIA, POWHEG
MINLO HJ+PYTHIA, and HRESgenerators as discussed in Section 3, are shown in blue, brown,
and pink, respectively. The sub-dominant component of the signal XH is indicated separately in green. In all estimations the total cross section is normalized to the SM estimate computed at NNLL+NNLO accuracy. Systematic uncertainties correspond to the accuracy of the gener-ators used to derive the differential estimations. The bottom panel shows the ratio of data or
theoretical estimates to the HREStheoretical estimations.
bative QCD calculations of the dominant loop-mediated gg → H production mechanism, in
which the transverse momentum pT(H) is expected to be balanced by the emission of soft
gluons and quarks. In addition, the rapidity distribution of the four-lepton system, y(H) is
sensitive both to the modelling of the gluon fusion production mechanism and to the PDFs of the colliding protons. The measured differential cross sections for these two observables are shown in Fig. 4. Results are compared to the theoretical estimations in which the dominant
gg→H contribution is modelled using POWHEG+JHUGEN, POWHEGMINLO HJ, and HRES.
In case of the HRES, the gg→ H acceptance is modelled at the parton level, and corrected for
the hadronization and underlying event effects in bins of the considered differential observ-able, as discussed in Section 3. The observed distributions are compatible with the SM-based theoretical estimations within the large associated uncertainties.
Similarly, the jet multiplicity N(jets), transverse momentum of the leading jet pT(jet), and its
separation in rapidity from the Higgs boson candidate|y(H) −y(jet)|are sensitive to the
the-oretical modelling of hard quark and gluon radiation in this process, as well as to the rela-tive contributions of different Higgs boson production mechanisms. The measured differential cross sections for the leading jet transverse momentum, and its separation in rapidity from the Higgs boson candidate are shown in Fig. 5, and are found to be compatible with the SM-based estimations within the large uncertainties. In the case of the jet multiplicity cross section, also shown in Fig. 5, we observe the largest deviation from the SM-based estimations. The p-value that quantifies the compatibility of the jet multiplicity distribution between data and SM
es-(jet) [fb/GeV] T /dp fid σ d -4 10 -3 10 -2 10 -1 10 1 (8 TeV) -1 19.7 fb CMS sys. unc.) ⊕
Data (stat. gg→H (POWHEG+JHUGen) + XH
Systematic uncertainty gg→H (MiNLO HJ) + XH
Model dependence XH = VBF + VH + ttH (jet) [GeV] T p 50 100 150 200 250 Ratio to MiNLO HJ 0 1 2 3 4 5 6 7 /d|y(H)-y(jet)| [fb] fid σ d 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 (8 TeV) -1 19.7 fb CMS sys. unc.) ⊕
Data (stat. gg→H (POWHEG+JHUGen) + XH
Systematic uncertainty gg→H (MiNLO HJ) + XH
Model dependence XH = VBF + VH + ttH |y(H)-y(jet)| 0 1 2 3 4 5 6 7 Ratio to MiNLO HJ 0 0.5 1 1.52 2.5 3 3.5 [fb] fid σ -2 10 -1 10 1 10 2 10 (8 TeV) -1 19.7 fb CMS sys. unc.) ⊕
Data (stat. gg→H (POWHEG+JHUGen) + XH
Systematic uncertainty gg→H (MiNLO HJ) + XH
Model dependence XH = VBF + VH + ttH N(jets) 0 1 2 ≥ 3 Ratio to MiNLO HJ 0 1 2 3 4 5
Figure 5: Results of the differential H → 4` fiducial cross section measurements and
com-parison to the theoretical estimates for the transverse momentum of the leading jet (top left), separation in rapidity between the Higgs boson candidate and the leading jet (top right), as well as for the jet multiplicity (bottom). The red error bars represent the systematic uncer-tainties, while black error bars represent the combined statistical and systematic unceruncer-tainties, summed in quadrature. The additional systematic uncertainty associated with the model de-pendence is separately represented by the grey boxes. Theoretical estimations, in which the
acceptance of the dominant gg→H contribution is modelled by POWHEG+JHUGEN+PYTHIA,
and POWHEGMINLO HJ+PYTHIAgenerators, as discussed in Section 3, are shown in blue and
brown, respectively. The sub-dominant component of the signal XH is indicated separately in green. In all estimations the total cross section is normalized to the SM estimate computed at NNLL+NNLO accuracy. Systematic uncertainties correspond to the accuracy of the genera-tors used to derive the differential estimations. The bottom panel shows the ratio of data or
theoretical estimates to the POWHEGMINLO HJ theoretical estimations.
timations is p = 0.13. It is computed from the difference between the −2 log(L) at its best
fit value and the value with the cross sections fixed to the theoretical estimation based on the POWHEG+JHUGENdescription of the gg →H process. Furthermore, we have performed the
measurement of the differential Z→ 4`cross sections at 8 TeV for the same set of observables
used in the H→4`measurements, including the jet multiplicity, and have found a good
18 9 Summary
events range from 0.21 in case of rapidity of the Z boson, to 0.99 for some of the angles de-fined by the four leptons in the Collins-Soper reference frame [64]. As the relative statistical
uncertainty in the Z → 4`measurement is lower than the relative uncertainty in the H → 4`
measurement, these results provide additional validation of the measurement procedure in data.
9
Summary
We have presented measurements of the integrated and differential fiducial cross sections for
the production of four leptons via the H → 4`decays in pp collisions at centre-of-mass
ener-gies of 7 and 8 TeV. The measurements were performed using collision data corresponding to
integrated luminosities of 5.1 fb−1at 7 TeV and 19.7 fb−1at 8 TeV. The differential cross sections
were measured as a function of the transverse momentum and the rapidity of the four-lepton system, the transverse momentum of the leading jet, the difference in rapidity between the Higgs boson candidate and the leading jet, and the jet multiplicity. Measurements of the
fidu-cial cross section for the production of four leptons via the Z → 4`decays, as well as its ratio
to the H→ 4`cross section, were also performed using the 8 TeV data. The uncertainty in the
measurements due to the assumptions in the model of Higgs boson properties was estimated by studying a range of exotic Higgs boson production and spin-parity models. It was found to be lower than 7% of the fiducial cross section. The integrated fiducial cross section for the
four leptons production via the H → 4` decays is measured to be 0.56+−0.670.44(stat) +−0.210.06(syst) fb
and 1.11+−0.410.35(stat)+−0.140.10(syst) fb at 7 and 8 TeV, respectively. The measurements are found to be
compatible with theoretical calculations based on the standard model.
Acknowledgements
We congratulate our colleagues in the CERN accelerator departments for the excellent perfor-mance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we grate-fully acknowledge the computing centres and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. Fi-nally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies: the Austrian Federal Min-istry of Science, Research and Economy and the Austrian Science Fund; the Belgian Fonds de la Recherche Scientifique, and Fonds voor Wetenschappelijk Onderzoek; the Brazilian Fund-ing Agencies (CNPq, CAPES, FAPERJ, and FAPESP); the Bulgarian Ministry of Education and Science; CERN; the Chinese Academy of Sciences, Ministry of Science and Technology, and Na-tional Natural Science Foundation of China; the Colombian Funding Agency (COLCIENCIAS); the Croatian Ministry of Science, Education and Sport, and the Croatian Science Foundation; the Research Promotion Foundation, Cyprus; the Ministry of Education and Research, Esto-nian Research Council via IUT23-4 and IUT23-6 and European Regional Development Fund, Estonia; the Academy of Finland, Finnish Ministry of Education and Culture, and Helsinki Institute of Physics; the Institut National de Physique Nucl´eaire et de Physique des Partic-ules / CNRS, and Commissariat `a l’ ´Energie Atomique et aux ´Energies Alternatives / CEA, France; the Bundesministerium f ¨ur Bildung und Forschung, Deutsche Forschungsgemeinschaft, and Helmholtz-Gemeinschaft Deutscher Forschungszentren, Germany; the General Secretariat for Research and Technology, Greece; the National Scientific Research Foundation, and Na-tional Innovation Office, Hungary; the Department of Atomic Energy and the Department
of Science and Technology, India; the Institute for Studies in Theoretical Physics and Mathe-matics, Iran; the Science Foundation, Ireland; the Istituto Nazionale di Fisica Nucleare, Italy; the Ministry of Science, ICT and Future Planning, and National Research Foundation (NRF), Republic of Korea; the Lithuanian Academy of Sciences; the Ministry of Education, and Uni-versity of Malaya (Malaysia); the Mexican Funding Agencies (CINVESTAV, CONACYT, SEP, and UASLP-FAI); the Ministry of Business, Innovation and Employment, New Zealand; the Pakistan Atomic Energy Commission; the Ministry of Science and Higher Education and the National Science Centre, Poland; the Fundac¸˜ao para a Ciˆencia e a Tecnologia, Portugal; JINR, Dubna; the Ministry of Education and Science of the Russian Federation, the Federal Agency of Atomic Energy of the Russian Federation, Russian Academy of Sciences, and the Russian Foun-dation for Basic Research; the Ministry of Education, Science and Technological Development of Serbia; the Secretar´ıa de Estado de Investigaci ´on, Desarrollo e Innovaci ´on and Programa Consolider-Ingenio 2010, Spain; the Swiss Funding Agencies (ETH Board, ETH Zurich, PSI, SNF, UniZH, Canton Zurich, and SER); the Ministry of Science and Technology, Taipei; the Thailand Center of Excellence in Physics, the Institute for the Promotion of Teaching Science and Technology of Thailand, Special Task Force for Activating Research and the National Sci-ence and Technology Development Agency of Thailand; the Scientific and Technical Research Council of Turkey, and Turkish Atomic Energy Authority; the National Academy of Sciences of Ukraine, and State Fund for Fundamental Researches, Ukraine; the Science and Technology Facilities Council, UK; the US Department of Energy, and the US National Science Foundation. Individuals have received support from the Marie-Curie programme and the European Re-search Council and EPLANET (European Union); the Leventis Foundation; the A. P. Sloan Foundation; the Alexander von Humboldt Foundation; the Belgian Federal Science Policy Of-fice; the Fonds pour la Formation `a la Recherche dans l’Industrie et dans l’Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-(FRIA-Belgium); the Ministry of Education, Youth and Sports (MEYS) of the Czech Republic; the Council of Science and Industrial Research, India; the HOMING PLUS programme of the Foundation for Polish Science, cofinanced from European Union, Regional Development Fund; the OPUS programme of the National Science Center (Poland); the Compagnia di San Paolo (Torino); the Consorzio per la Fisica (Trieste); MIUR project 20108T4XTM (Italy); the Thalis and Aristeia programmes cofinanced by EU-ESF and the Greek NSRF; the National Priorities Research Program by Qatar National Research Fund; the Rachadapisek Sompot Fund for Postdoctoral Fellowship, Chula-longkorn University (Thailand); and the Welch Foundation, contract C-1845.
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